Consider the following equation. 3x4 − 8x3 + 6 = 0, [2, 3] (a) Explain how we know that the given equation must have a root in the given interval. Let f(x) = 3x4 − 8x3 + 6. The polynomial f is continuous on [2, 3], f(2) = < 0, and f(3) = > 0, so by the Intermediate Value Theorem, there is a number c in (2, 3) such that f(c) = . In other words, the equation 3x4 − 8x3 + 6 = 0 has a root in [2, 3]. (b) Use Newton's method to approximate the root correct to six decimal places.

Answer:

  A. Integers

Step-by-step explanation:

Subtraction of whole or natural numbers can result in a negative number that is not in the set. Subtraction of irrational numbers can result in a rational number (√2 -√2 = 0, for example).

Final answer:

The Integers are closed under subtraction because the difference of any two integers is always an integer, while Whole Numbers, Natural Numbers, and Irrational Numbers are not, as their differences can result in numbers outside of their respective sets. Therefore, the correct answer is A.

Explanation:

When considering which of the following sets is closed under subtraction, we must understand what it means for a set to be 'closed' under an operation. A set is closed under subtraction if, when you subtract any two elements in the set, the result is also an element of the set.

Integers include whole numbers as well as their negative counterparts, such as -1, 0, and 1. When you subtract any two integers, the result is always another integer. Therefore, the set of integers is closed under subtraction.

Whole numbers, on the other hand, include 0 and all the positive integers. Subtracting a larger whole number from a smaller one would result in a negative integer, which is not included in the set of whole numbers. Thus, this set is not closed under subtraction.

Natural numbers are like whole numbers but don't include 0. Just like whole numbers, subtracting a larger natural number from a smaller one would result in a negative integer, which is not a natural number. Hence, natural numbers are not closed under subtraction.

Irrational numbers include quantities like π and √2. Subtracting two irrational numbers might result in a rational number, which is not an irrational number. Therefore, the set of irrational numbers is not closed under subtraction.

Therefore, the correct answer is A. Integers.

Answer:

Step-by-step explanation:

A) the slope values you have put in your problem statement are correct. As you know, they are computed from ...

  (change in gallons)/(change in time)

where the reference point for changes is P. Using the first listed point Q as an example, the secant slope is ...

  (3410 -1275)/(5 -15) = 2135/-10 = -213.5 . . . . gallons per minute

__

B) The average of the secant slopes for points Q adjacent to P is ...

  (-187 +(-145))/2 = -332/2 = -166 . . . . gallons per minute

The tangent slope at point P is estimated at -166 gpm.

The secant line joins two points on the curve of a graph.

Point P is given as:

[tex]P = (15,1275)[/tex]

(a) The slopes of the secant lines PQ

The points are given as:

[tex]Q = \{(5,3410),(10, 2210),(20, 550) ,(25, 145),(30, 0) \}[/tex]

The slope (m) is calculated using:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

So, we have:

For Q = (5,3410), the slope of the secant line is:

[tex]m_1 = \frac{1275 - 3410}{15 - 5}[/tex]

[tex]m_1 = \frac{-2135}{10}[/tex]

[tex]m_1 = -213.5[/tex]

For Q = (10, 2210), the slope of the secant line is:

[tex]m_2 = \frac{1275 - 2210}{15 - 10}[/tex]

[tex]m_2 = \frac{-935}{5}[/tex]

[tex]m_2 = -187[/tex]

For Q = (20, 550), the slope of the secant line is:

[tex]m_3 = \frac{1275 - 550}{15 - 20}[/tex]

[tex]m_3 = \frac{725}{-5}[/tex]

[tex]m_3 = -145[/tex]

For Q = (25, 145), the slope of the secant line is:

[tex]m_4 = \frac{1275 - 140}{15 - 25}[/tex]

[tex]m_4 = \frac{1135}{-10}[/tex]

[tex]m_4 = -113.5[/tex]

For Q = (30, 0), the slope of the secant line is:

[tex]m_5 = \frac{1275 - 0}{15 - 30}[/tex]

[tex]m_5 = \frac{1275}{-15}[/tex]

[tex]m_5 = -85[/tex]

(b) The slope of the tangent by average

The closest secant lines to tangent P are

[tex]Q = \{(10, 2210),(20, 550)\}[/tex]

This is so, because point P (15, 1275) is between the above points.

The slopes of secant lines at [tex]Q = \{(10, 2210),(20, 550)\}[/tex] are:

[tex]m_2 = -187[/tex]

[tex]m_3 = -145[/tex]

The average slope (m) is:

[tex]m = \frac{m_2 + m_3}{2}[/tex]

[tex]m = \frac{-187 - 145}{2}[/tex]

[tex]m = \frac{-332}{2}[/tex]

[tex]m = -166[/tex]

Hence, the average slope is -166

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1 < x < 3 because

( x < 3 ) intersecting ( x > 1)

For this case we must find the intersection of the following inequations:

[tex]x + 1 <4\\x-8> -7[/tex]

So:

[tex]x + 1 <4\\x <4-1\\x <3[/tex]

All values of "x" less than 3.

[tex]x-8> -7\\x> -7 + 8\\x> 1[/tex]

All values of "x" greater than 1.

Thus, the intersection of the equations will be given by the values of "x" greater than 1 and less than 3.

[tex](1 <x <3)[/tex]

ANswer:[tex](1 <x <3)[/tex]

Answer:

Option B

Step-by-step explanation:

we know that

The sum of an arithmetic series is equal to

S=n(a1+an)/2

where

a1 is the first term

an is the last term

n is the number of terms

In this problem we have

n=20

a1=102

an=159

substitute the values in the formula

S=20(102+159)/2

Answer:

2.29%

Step-by-step explanation:

1. Chance of landing on black for one spin:

There are 38 spaces, and 18 lead to the wanted result. That means the chance is ¹⁸/₃₈, or about 0.47.

2. Chance for 5 spins.

We need to find (0.47)⁵, which is about 0.0229, which is 2.29%

That is none of the choices, but from every way I did this problem, that is the only solution I got.

As near as I can tell, you're given the vector field

[tex]\vec F(x,y,z)=\langle y,-x,14\rangle[/tex]

and that [tex]S[/tex] is the part of the upper half of the sphere with equation

[tex]x^2+y^2+z^2=4[/tex]

with boundary [tex]C[/tex] the circle in the plane [tex]z=0[/tex].

Parameterize [tex]C[/tex] by

[tex]\vec r(t)=\langle2\cos t,2\sin t,0\rangle[/tex]

with [tex]0\le t\le2\pi[/tex]. Then the line integral of [tex]\vec F(x,y,z)[/tex] along [tex]C[/tex] is

[tex]\displaystyle\int_C\vec F(x,y,z)\cdot\mathrm d\vec r=\int_0^{2\pi}\langle2\sin t,-2\cos t,14\rangle\cdot\langle-2\sin t,2\cos t,0\rangle\,\mathrm dt[/tex]

[tex]=\displaystyle-4\int_0^{2\pi}(\sin^2t+\cos^2t)\,\mathrm dt=\boxed{-8\pi}[/tex]

Parameterize [tex]S[/tex] by

[tex]\vec s(u,v)=\langle2\cos u\sin v,2\sin u\sin v,2\cos v\rangle[/tex]

with [tex]0\le u\le2\pi[/tex] and [tex]0\le v\le\dfrac\pi2[/tex]. We have

[tex]\nabla\times\vec F(x,y,z)=\langle0,0,-2\rangle[/tex]

Take the normal vector to [tex]S[/tex] to be

[tex]\vec s_v\times\vec s_u=\langle4\cos u\sin^2v,4\sin u\sin^2v,2\sin2v\rangle[/tex]

Then the surface integral of the curl of [tex]\vec F(x,y,z)[/tex] across [tex]S[/tex] is

[tex]\displaystyle\iint_S(\nabla\times\vec F(x,y,z))\cdot\mathrm d\vec S=\iint_S(\nabla\times\vec F(x(u,v),y(u,v),z(u,v)))\cdot(\vec s_v\times\vec s_u)\,\mathrm du\,\mathrm dv[/tex]

[tex]=\displaystyle\int_0^{\pi/2}\int_0^{2\pi}\langle0,0,-2\rangle\cdot\langle4\cos u\sin^2v,4\sin u\sin^2v,2\sin2v\rangle\,\mathrm du\,\mathrm dv[/tex]

[tex]=\displaystyle-4\int_0^{\pi/2}\int_0^{2\pi}\sin2v\,\mathrm du\,\mathrm dv=\boxed{-8\pi}[/tex]

Answer:

  x = 15°

Step-by-step explanation:

m∠DFQ = m∠OFQ = 52° (given), so arc DQ = 2·52° = 104°. Then arc FQ is the supplement of that, 180° -104° = 76°. The given relation to x is then ...

  76° = 5x +1°

  75° = 5x . . . . . . . subtract 1°

  15° = x . . . . . . . . .divide by 5

Answer:

3:45 PM

Step-by-step explanation:

The least common multiple of 3, 5, and 6 is 30, so the next occurrence will be 30 minutes after 3:15 PM, at 3:45 PM.

Answer:  The next time at which the three sounds will happen simultaneously at 3 : 45 PM.

Step-by-step explanation:  Given that Max sneezes every 5 minutes, Lina coughs every 6 minutes and their dog barks every 3 minutes.

We are to find the time at which these three sounds will happen simultaneously if there was sneezing, barking, and coughing at 3:15 PM.

We have

the sneezing, barking and coughing happen simultaneously at an interval that is equal to the L.C.M. of 5, 6 and 3 minutes.

Now,

L.C.M. (5, 6, 3) = 30.

Therefore, the sneezing, barking and coughing happen simultaneously at an interval of 30 minutes.

Since there was sneezing, barking, and coughing at 3:15 PM, so the next time at which the three sounds will happen simultaneously is

3 : 15 PM + 30 min = 3 : 45 PM.

Thus, the next time at which the three sounds will happen simultaneously is 3 : 45 PM.

Answer:

The amount of water left in the tank is approximately 58.1 cubic meters

Step-by-step explanation:

step 1

Find the volume of the a cube shape tank

The volume is equal to

[tex]V=b^{3}[/tex]

we have

[tex]b=4.6\ m[/tex]

substitute

[tex]V=4.6^{3}=97.336\ m^{3}[/tex]

step 2

Find the volume of cone

The volume is equal to

[tex]V=\frac{1}{3}\pi r^{2}h[/tex]

we have

[tex]r=2.5\ m[/tex]

[tex]h=6\ m[/tex]

[tex]\pi =3.14[/tex]

substitute

[tex]V=\frac{1}{3}(3.14)(2.5)^{2}(6)[/tex]

[tex]V=39.25\ m^{3}[/tex]

step 3

Find the difference of the volumes

[tex]97.336\ m^{3}-39.25\ m^{3}=58.1\ m^{3}[/tex]

Answer:

[tex](f-g)(x)=4x^{4}+2x^3}-2x-4[/tex]

Step-by-step explanation:

Let f and g be two functions that are defined in the same interval and have the same independent variable. Then, the Subtraction of Function is defined as:

[tex](f-g)(x)=f(x)-g(x)[/tex]

Let's solve (f-g)(x) with [tex]f(x)=5x^{4}+4x^3}+3x^{2}+2x+1[/tex] and [tex]g(x)=x^{4}+2x^{3}+3x^{2}+4x+5[/tex]

[tex](f-g)(x)=(5x^{4}+4x^3}+3x^{2}+2x+1)-(x^{4}+2x^{3}+3x^{2}+4x+5)\\(f-g)(x)=5x^{4}+4x^3}+3x^{2}+2x+1-x^{4}-2x^{3}-3x^{2}-4x-5\\(f-g)(x)=4x^{4}+2x^3}-2x-4[/tex]

.

Answer:

A. The maximum height of the volleyball was 23 feet.

Step-by-step explanation:

Given the equation for the height as

f(x) = -2(t - 3) +23

The time taken to attain maximum height = 3 seconds

Finding the maximum height; we substitute value of t with 3 sec in the function;

f(x) = -2(t - 3) +23

f(3) = -2(3-3) +23

maximum height= 23

Answer:

10 hours

Step-by-step explanation:

If I have $50 in my bank account, and I want to have a total of $130 in my account. It means that I need to work enough hours to make $130 - $50 = $80.

If I make $8 per hour, and I need to make $80, then I just have to work 10 hours. ($80/8 = 10)

Answer:

A. 280

B. 185

Step-by-step explanation:

A. Buying price of share stock= $ 225

Profit = $55

Selling price= Buying price + profit

[tex]= 225+ 55= 280[/tex]

Selling price= $280

B.

Decrease in price was by $40

Buying price= $225

New selling price if he had waited till then will be=

[tex]= 225-40 = 185[/tex]

=$185

Answer:

5t/3

Step-by-step explanation:

r^8=5 and r^7=3/t

here r^8=5

r^7×r=5

3/t×r=5

r=5t/3

The value of r in terms of t is 5t/3.

A term written aˣ is an exponential term. Its value is obtained by multiplying a with itself x number of times. The term aˣ is read as

a raised to the power of x.

Given r⁸ = 5, r⁷ = 3/t. We are asked to determine the value of r in terms of t.

We will apply the exponential rule [tex]\frac{x^{a} }{x^b} = x^{a-b}[/tex].

Let our equations be r⁸ = 5 ... (1), and r⁷ = 3/t ... (2).

Dividing (1) by (2), we get

r⁸/r⁷ = 5/(3/t)

or, r⁸-⁷ = 5t/3 (using the rule [tex]\frac{x^{a} }{x^b} = x^{a-b}[/tex] )

or, r = 5t/3.

∴ The value of r in terms of t is 5t/3.

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Period of a function is [tex]2\pi[/tex]. You can see on graph, the distance between two points lying on intersection with x axis and function is [tex]2\pi[/tex] so A would be an answer.

Answer:

you would have 24 slices of bread

Step-by-step explanation:

(12 in)/(1/2 in/slice) = 12·2/1 slices = 24 slices

Answer:

[tex]A=\$5003.2[/tex]

Step-by-step explanation:

Use the exponential growth formula

[tex]A = Pe ^ {rt}[/tex]

Where A is the final amount in the account, P is the initial amount, r is the growth rate and t is the time in years

In this problem

We know that

[tex]P=4,200\\\\r=\frac{3.5\%}{100\%}= 0.035\\\\ t=5\ years[/tex]

So

[tex]A = 4,200e^{0.035t}[/tex]

Finally after 5 years the balance of the account is:

[tex]A=\$5003.2[/tex]

Try this:

if x=13 it means 'one solution'; the only point;

if 0=13 it means 'no solution'; wrong equation = no points;

if 0=0 it means 'many solutions'; no variable in the equation = much points.

Finally:

System #1 - one solution;

System #2 - no solution;

System #3 - many solutions.

Answer:

  C. -4n + 8

Step-by-step explanation:

Try the formulas and see which works.

__

The common difference is -4, so the coefficient of n in the explicit formula is -4. Every term is divisible by 4, so there won't be 3 anywhere in the formula.

__

-4·1 +8 = 4

-4·2 +8 = 0

-4·3 +8 = -4

-4·4 +8 = -8

The formula -4n+8 reproduces the sequence exactly.

The function crosses the x-axis at points (-4,0), (-1,0), (2,0), and (5,0).

The amplitude is a measure of how far the function oscillates from its equilibrium position (usually the x-axis). Here are the steps to find the amplitude:

1. Identify the Peaks and Troughs:

  - Observe the graph and locate the highest point (peak) and the lowest point (trough) of the waveform.

  - In our case:

    - Peak (Maximum Point) = 5

    - Trough (Minimum Point) = -3

2. Calculate the Amplitude:

  - The amplitude can be found using the formula:

[tex]\[ \text{Amplitude} = \frac{\text{Peak} - \text{Trough}}{2} \][/tex]

  - Substituting the values:

[tex]\[ \text{Amplitude} = \frac{5 - (-3)}{2} = \frac{8}{2} = 4 \][/tex]

Therefore, based on visual estimation, the amplitude of this wave is approximately 4.

3. Graphical Representation:

  - The graph represents a sinusoidal function with two complete cycles visible.

  - Peaks occur at approximately (y = 5), and troughs occur at approximately (y = -3).

  - The function crosses the x-axis at points (-4,0), (-1,0), (2,0), and (5,0).

Answer with explanation:

[tex]\text{Average}=\frac{\text{Sum of all the observation}}{\text{Total number of Observation}}[/tex]

Average Height of tallest Building in San Francisco

                    [tex]=\frac{260+237+212+197+184+183+183+175+174+173}{10}\\\\=\frac{1978}{10}\\\\=197.8[/tex]

Average Height of tallest Building in Los Angeles

                    [tex]=\frac{310+262+229+228+224+221+220+219+213+213}{10}\\\\=\frac{2339}{10}\\\\=233.9[/tex]

→→Difference between Height of tallest Building in Los Angeles and  Height of tallest Building in San Francisco

               =233.9-197.8

               =36.1

⇒The average height of the 10 tallest buildings in Los Angeles is 36.1 more than the average height of the tallest buildings in San Francisco.

⇒Part B

Mean absolute deviation for the 10 tallest buildings in San Francisco

 |260-197.8|=62.2

 |237-197.8|=39.2

 |212-197.8|=14.2

 |197 -197.8|= 0.8

 |184 -197.8|=13.8

 |183-197.8|=14.8

 |183-197.8|= 14.8

 |175-197.8|=22.8

 |174-197.8|=23.8

 |173 -197.8|=24.8

Average of these numbers

     [tex]=\frac{62.2+39.2+14.2+0.8+13.8+14.8+14.8+22.8+23.8+24.8}{10}\\\\=\frac{231.2}{10}\\\\=23.12[/tex]

Mean absolute deviation=23.12

Answer:

1st -36.1 meters or more

2nd -23.12

Step-by-step explanation:

ANSWER

[tex]g(x) = {x}^{2} + 4x + 4[/tex]

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} - 6x + 9[/tex]

This can be rewritten as:

[tex]f(x) = {(x - 3)}^{2} [/tex]

If this function is shifted 5 units to the left to create g(x), the

[tex]g(x) = f(x + 5)[/tex]

We substitute x+5 into f(x) to get:

[tex]g(x) = {(x + 5 - 3)}^{2} [/tex]

[tex]g(x) = {(x + 2)}^{2} [/tex]

We expand to get:

[tex]g(x) = {x}^{2} + 4x + 4[/tex]

Answer:

g(x) = x^2 + 4x + 4

Step-by-step explanation:

In translation of functions, adding a constant to the domain values (x) of a function will move the graph to the left, while subtracting from the input of the function will move the graph to the right.

Given the function;

f(x) = x2 - 6x + 9

a shift 5 units to the left implies that we shall be adding the constant 5 to the x values of the function;

g(x) = f(x+5)

g(x) = (x+5)^2 - 6(x+5) + 9

g(x) = x^2 + 10x + 25 - 6x -30 + 9

g(x) = x^2 + 4x + 4

Answer:

In the year 2010, the population of the city was 175,000

Step-by-step explanation:

If we rewrote this as a linear expression in standard form (it is linear, btw), it would look like this:

[tex]P(t)=\frac{11}{2}t+175[/tex]

The rate of change, the slope of this line, is 11/2.  If the year 2010 is our time zero (in other words, we start the clock at that year), then 0 time has gone by in the year 2010.  In the year 2011, t = 1 (one year goes by from 2010 to 2011); in the year 2012, t = 2 (two years have gone by from 2010 to 2012), etc.  If we plug in a 0 for t we get that y = 175,000.  That is our y-intercept, which also serves to give us the starting amount of something time-related when NO time has gone by.

What is the problem about? Does x equal 24 in the problem?

Normally, x is an unknown variable that needs to be evaluated, so I don’t really know what x is at the moment. Please show me the problem so that I can solve the equation.

Answer:

(4,7)

Step-by-step explanation:

3x+x+3=19

4x=16

x=4

so y=7

c. (4,7)

a)

[tex]x^2+y^2-2x+2y-1=0[/tex]

It could be expressed as:

[tex](x-1)^2-1+(y+1)^2-1-1=0\\\\\\i.e.\\\\\\(x-1)^2+(y+1)^2=3\\\\\\i.e.\\\\\\(x-1)^2+(y+1)^2=(\sqrt{3})^2[/tex]

Hence, the radius of circle is: √3≈1.732 units

b)

[tex]x^2+y^2-4x+4y-10=0[/tex]

It is represented as:

[tex](x-2)^2-4+(y+2)^2-4-10=0\\\\\\i.e.\\\\\\(x-2)^2+(y+2)^2=18\\\\\\(x-2)^2+(y+2)^2=(3\sqrt{2})^2[/tex]

Hence, the radius of circle is: 3√2≈4.242 units

c)

[tex]x^2+y^2-8x-6y-20=0[/tex]

on converting to standard form

[tex](x-4)^2+(y-3)^2=(3\sqrt{5})^2[/tex]

Hence, the radius of circle is: 3√5≈6.708 units

d)

[tex]4x^2+4y^2+16x+24y-40=0[/tex]

on dividing both side by 4 we obtain:

[tex]x^2+y^2+4x+6y-10=0\\\\\\(x+2)^2+(y+3)^2=(\sqrt{23})^2[/tex]

Hence, radius of circle is: √23=4.796 units

e)

[tex]5x^2+5y^2-20x+30y+40=0[/tex]

on dividing both side by 5 we obtain:

[tex]x^2+y^2-4x+6y+8=0[/tex]

[tex](x-2)^2+(y+3)^2=(\sqrt{5})^2[/tex]

Hence, radius of circle is: √5=2.236 units

f)

[tex]2x^2+2y^2-28x-32y-8=0[/tex]

which could also be represented as follows:

[tex]x^2+y^2-14x-16y-4=0\\\\\\(x-7)^2+(y-8)^2=(\sqrt{117})^2[/tex]

Hence, the radius of circle is: [tex]\sqrt{117}[/tex]≈ 10.817 units

g)

[tex]x^2+y^2+12x-2y-9=0[/tex]

It could also be written as:

 [tex](x+6)^2+(y-1)^2=(\sqrt{46})^2[/tex]

Hence, the radius of circle is: [tex]\sqrt{46}[/tex]≈ 6.782 units

            The ascending order is:

        a → e → b → d → c → g → f

The radius of a circle can be found from its equation in general form, which can be rearranged into the format (x-h)² + (y-k)² = r². From there, the radii of all the circles can be determined, and the circles arranged in ascending order by these lengths.

To arrange the circles in ascending order of their radii, we need to understand the general equation of a circle which is in the format "(x-h)² + (y-k)² = r²". Here, (h,k) are the coordinates of the center of the circle, and 'r' is the radius of the circle. The given equations of the circles usually can be rewritten into this format.

To ascertain the radius of a circle from its equation, identify the constant term on the right hand side of the equation, which is the square of the radius (r²). The square root of this term will give you the 'r' - radius of the circle.

Once you know the radii of all the circles, arrange the equations in ascending order of these radii value. Remember, the smaller the r, the smaller the circle's circumference and area.

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Answer:

The answers to a, b, d, e, g are correct (as noted in your problem statement).

Step-by-step explanation:

a) The triangles are similar because their apex angle is the same angle, and their base angles are corresponding angles where transversals cross parallel lines, hence congruent. The triangles are similar by AA (or AAA, if you like) since all corresponding angles are congruent.

__

b) GE = OE -OG = 5.8 -435 = 1.45 . . . cm

__

c) Technically speaking, there is not enough information in your posted question to allow TS to be found. You can find the length TU using the Pythagorean theorem. (First you need OU (see g below).) By that theorem, ...

TU^2 + OU^2 = OT^2

TU = √(OT^2 -OU^2) = √(2^2 -1.8^2) = √0.76 ≈ 0.87

By all appearances, US = TU. If you make that assumption, then ...

TS = 2·TU = 2·0.87 = 1.74 . . . cm

__

d) We have seen that OG = 3·GE, so OA will be 3·AU.

OA = 3·AU = 3·0.45 = 1.35 . . . cm

__

e) Using the same proportions we have observed elsewhere,

BT/OT = 1/4

BT = (2 cm)/4 = 0.5 cm

__

f) SE = TE - TS = 6 cm - 1.74 cm = 4.26 cm

(see part (c) above for the assumption we must make regarding this)

__

g) OU = OA + AU = 1.35 cm + 0.45 cm = 1.8 cm

Answer:

  see below

Step-by-step explanation:

Each point moves to twice its original distance from (-4, -3). The point (-4, -3) remains unmoved.

Answer: (-4,1) ; (2,-3) ; (-4,-3)

Answer:

1131.0 m^3

Step-by-step explanation:

Let h1 represent the height of the top cone, and h2 the height of the bottom cone. The volume of a cone is given by the formula ...

V = (1/3)πr^2·h

so the volumes of both cones together will be ...

V = (1/3)πr^2·h1 + (1/3)πr^2·h2 = (1/3)πr^2·(h1 +h2)

= (1/3)π(6 m)^2(12 m + 18 m) = 360π m^3

≈ 1131.0 m^3

The answer is:

The difference between the areas of the circles will be:

[tex]Difference=36\pi -9\pi =27\pi[/tex]

To find the diffence in area between the two circles, we need to find both areas and then, subtract the smallest circle area to the largest circle area.

So,

For the small circle, we have:

[tex]Area_{SmallCircle}=\pi *radius^{2} \\\\Area_{SmallCircle}=\pi *(3)^{2}=9\pi[/tex]

For the large circle, we have:

[tex]Area_{LargeCircle}=\pi *radius^{2} \\\\Area_{LargeCircle}=\pi *(6)^{2}=36\pi[/tex]

Hence, we have that the difference between the areas of the circles will be:

[tex]Difference=36\pi -9\pi =27\pi[/tex]

Have a nice day!

Answer:

Difference = 27π square units

Step-by-step explanation:

Points to remember

Area of circle = πr²

Where r - Radius of circle

To find the area of large circle

Here r = 6 units

Area = πr²  = π * 6²

 = 36π square units

To find the area of small circle

Here r = 3 units

Area = πr²  = π * 3²

 = 9π square units

To find the difference

Difference = area of large circle - area of small circle

 = 36π - 9π = 27π square units